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Cut base off of lettuce heads. Gently peel off leaves, wash, and pat dry with paper towels. Refrigerate until ready to serve the dish.
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Season chicken well with salt and pepper.
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In a large skillet, heat 1 tablespoon oil over high heat. Add the chicken; cook, stirring constantly, until opaque throughout, 6 to 8 minutes. Transfer to a plate.
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Add remaining 1 tablespoons of oil to pan, along with the onion and bell pepper. Reduce heat to medium. Cook, stirring constantly, until onion is tender and golden, about 6 minutes.
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Add garlic, ginger, orange peel, and red-pepper flakes and water chestnuts; cook, stirring, until fragrant, 30 to 60 seconds.
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While garlic/ginger mixture is cooking, whisk the cornstarch and water together in a bowl. Add in the soy sauce, vinegar, and hoisin sauce; whisk.
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Pour cornstarch mixture over garlic/ginger mixture. Reduce heat to low. Add chicken to pan and toss to coat.
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Serve the chicken mixture wrapped in the lettuce leaves.